As is seen, the first-order model (REF ) is gauge theory of
special form in the whole range (REF ) of admissible
values of the parameters \(\alpha \) , \(\beta \) . Equation (REF )
determines the least action principle for the model. The
quantization of this theory can be performed by means of the
well-known procedures [1]}. In all the instances with bounded
from below Hamiltonian, we expect the stability of the model. This
means that equations (REF ) determine a higher derivative
theory, which can be stable at classical and quantum level. Because
of existence of first-order formalism, the model is as good as the
Lagrangian theories. In particular, it admits consequent
quantization, and correspondence between symmetries and conserved
quantities. The Hamiltonian serves as quantity that is associated to
the invariance of the model (REF ) with respect to the time
translations. The Hamiltonian (REF ) is on-shell bounded if
the conditions (REF ) are satisfied.
